Problem: If $x \bigtriangleup y = 2x^{2}+y^{2}$ and $x \veebar y = x(y-7)$, find $-2 \veebar (1 \bigtriangleup -1)$.
Answer: First, find $1 \bigtriangleup -1$ $ 1 \bigtriangleup -1 = 2(1^{2})+(-1)^{2}$ $ \hphantom{1 \bigtriangleup -1} = 3$ Now, find $-2 \veebar 3$ $ -2 \veebar 3 = -2(3-7)$ $ \hphantom{-2 \veebar 3} = 8$.